The world in 389 AD was a different place. The Roman Empire was on the verge of collapsing, and the world was in turmoil. Between barbarian invasions and a skyrocketing death rates, it’s little wonder that people believed it was the end of the world. Amidst this chaos, on the rim of the Mediterranean, the philosopher Saint Augustine of Hippo pondered the meaning of teaching. To a modern reader, his essay De Magistro may appear archaic. He believed that teaching was a form of remembering, and that nothing could not be taught that wasn’t already known. To illustrate this, he asks his pupil, who is also his son, several questions that seek to demonstrate the meaning of signs, like words and gestures. He asks him to demonstrate how he could teach somebody what walking means without using words or signs. His pupil replies that he could do the action of walking, and then someone would know what the word “walking” means. Augustine replies that the person might think it means any number of things, such as standing up, or swinging ones arms, or moving in a circle, but that the exact meaning of walking might escape them unless they had already conceptualized walking.

This all seems a bit esoteric, but he is trying to make a deep point (at least he thought it was), and this point is that we cannot learn anything that we don’t already know. He believes that unless we had an idea about what walking already was, then we wouldn’t be able to understand what the teacher was trying to tell us. This is a, if not the, fundamental challenge of teaching, but it's also a challenge simply interacting with other cultures. Some cultural ideas may take years for an outsider to translate successfully. Don't think it's true? Try explaining what "hokey" means without referring to Hee-Haw.

One way to think about what Augustine is trying to get at is to imagine encounters with alien races. If an alien tried to teach us something that was within its (assuming it's gender neutral) conceptual repertoire but not in ours, it might be impossible for us to learn it. The alien could tell us its word for the concept ("splugdorfffs"), and maybe it could give us a physical example by puffing air through its tentacles until its antennae vibrated. How would we know exactly what would it be trying to communicate? Is it using the vibrating antennae as metaphor for a feeling, an allusion to a type of initiation ritual, or to an actual physical motion? What if it was trying to teach us how it feels to give birth to a nest of eggs while metamorphosing into another creature? What if it was trying to tell us something that I cannot even describe in human language? As Augustine is wrestling with, can we actually learn something if we don't have the concept somewhere in buried in our brain?

If we eventually could learn the concept from the alien, then I think Augustine would argue that it was because we built the concept out of other, more fundamental, concepts. We know what it's like to walk, so if the alien was teaching us about walking on nine legs we could extend our concept of walking on two. We know what it's like to lose something and we have a concept of honor, so if it was teaching us about the honor of losing one's wings in battle with the fire jackals, then we could probably get the gist. But what if it was trying to teach us a concept that wasn't composed of other concepts within our language and thought paradigm? Could we eventually learn this concept, and if so, how?

Augustine believed that these original concepts came from God, and that only by God's light do we really know something. His philosophy gets mixed up with neo-Platonism at this point, which was the thing to do in the 4th century AD. His theory was that first God invests us with the original concepts, and then a teacher uses signs to draw these concepts out and connect them in a way that makes sense to us; however, the teacher can never impart something that isn’t already there. This innate versus learned debate is still with us (see Chomsky versus Skinner for a 20th century take on it). I think this debate is also still relevant to modern learning theory. Constructivism posits that students build their own internal knowledge structures, and that these structures are the foundation for new knowledge acquisition. But where did the initial foundation come from?

I think (with very little reference to evidence because this is a blog and not a full article) that they come from the fundamental plan of our nervous system. The initial sensory information, such as sight, touch, pain, or acceleration, then become the building blocks refined through early education. Interestingly, the sensory information that is presented to our brain is already highly refined, and these basic concepts are built into it. An image, for example, is built from separate neural circuits for color, line, and movement, that our brain builds into an image and presents as a whole to our consciousness. Oddly, we can conceptually unpack the whole and examine each separately. All visual knowledge ultimately relies on these components, which are hardwired into our visual processing system.

So to return to Augustine, could we be taught a visual concept outside of color, line, and movement? Are there completely different ways for neurons to interpret visual information and present them to consciousness, and if so, how could we ever learn them? It's the philosophical question posed by every teenager: is your red the same as mine? But what if the experience of red isn't even in our sensory modality suite? This seems impossible to me, and maybe it puts a limit on what a human being can learn; perhaps Augustine is right and we can only learn things that we already have a concept for, but instead of God putting them there it's evolution.

In the classroom I've pondered the pragmatic implications of this. When trying to teach students about blood pressure, it's always a bit surprising to me how few of them have a real concept of pressure in general. They know the word, and they know how to use it in a sentence, but when I ask them to explain it their understanding fails them. I end up having them press on their arms with a book or with a pencil point using about the same force, and we talk about how force is spread out over an area. Basically, I end up teaching them about blood pressure by engaging their primary sensory modality so that they can link this sensory information to the concept of pressure and then extrapolate it to the inner wall of a blood vessel. I think the concept was already there in the neural wiring, but they hadn't perceived it for what it was. So maybe I buy into Augustine's argument.

My own intuition (which is likely wrong, and once I do the research I'll post it here) is that experts in a field become adept at linking these primary concepts up to increasingly abstract concepts. Without these links down, thought becomes increasingly abstract and difficult to follow. A physician likely has many hundreds of primary sensory experiences that are linked to the concept of blood pressure: feeling it thud in a pulse, watching a vessel spurt during a surgery, pressing against a bleeding wound. These sensory experiences refine and build the knowledge base required for understanding more abstract concepts related to blood pressure. The formal is constantly being rooted by the concrete.

It is beyond the scope of my teaching, but for fields in which the concepts are so abstract they can only be represented with mathematics, the difficulty in teaching must be extreme. How do we find concepts to link when there are no concrete sensory experiences from which to pull? Finally, I wonder what Augustine would have made of his argument had he not believed in God and seen the creation of our original concepts from an evolutionary point of view, slowly being refined by natural selection until they work well enough to increase fitness, but not necessarily more so.